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The discovery of all possible ways to tie a tie depends on a mathematical formulation of the act of tying a tie. In their papers (which are technical) and book (which is for a lay audience, apart from an appendix), the authors show that necktie knots are equivalent to persistent random walks on a triangular lattice, with some constraints on how the walks begin and end.
Hitching tie – simple knot used to tie off drawstring bags that allows quick access; Honda knot a.k.a. lariat loop – loop knot commonly used in a lasso; Hoxton knot – a method of arranging a scarf about the neck; Hunter's bend a.k.a. rigger's bend – joins two lines
A small knot. The small knot, also known as oriental knot, Kent knot, or simple knot, is the simplest method of tying a necktie. Unlike the Four-in-hand knot and Windsor knot, the small knot is not self-releasing. The small knot is tied inside out, though this can be mitigated by giving the tie a half-twist during the tying process.
The Windsor knot, sometimes referred to as a full Windsor (or misleadingly as a double Windsor) to distinguish it from the half-Windsor, is a knot used to tie a necktie.As with other common necktie knots, the Windsor knot is triangular, and the wide end of the tie drapes in front of the narrow end.
In other cases, a knot being tied in the bight is a matter of the method of tying rather than a difference in the completed form of the knot. For example, the clove hitch can be made "in the bight" if it is being slipped over the end of a post but not if being cast onto a closed ring, which requires access to an end of the rope.
Friction knots are held in place by the friction between the windings of line. Knotted-ends knots are held in place by the two ends of the line being knotted together. Stopping may be either a temporary whipping or seizing, the commonest variety consisting of a few round turns finished off with a reef knot .
Tie an overhand knot at the end of a rope but do not tighten the knot down. Pass the end of the line through the loop created by the first overhand knot. Tighten the knot down while sliding it into place at the end of the line. Be sure to leave some tail sticking out from the end of the knot. [7] [8]
For mountaineers/climbers, there tends to be a strong preference for using knots that are perceived to be relatively easy to tie - even when fatigued or in a less than optimal frame of mind [clarification needed] - and so #1410 (Offset overhand bend) is favored. Climbers/canyoners need to retrieve their ropes after an abseil/rappel descent.